Auto-tuning of filtered proportional-integral-derivative controller for industrial processes under routine operating conditions

In general, auto-tuning implementation of PID controllers relies on dual controllers, exciting/identification experiments or some prior knowledge on the process and hence the considerable cost on auto-tuning implementation occurs. To deal with such a problem, a new auto-tuning scheme of the FPID controller is developed for minimum variance tasks under routine operating conditions in which the closed-loop system is running without any external excitation other than natural disturbances. This paper reveals that the stochastic disturbance model can be uniquely determined from the first several terms of the impulse response coefficients of the closed-loop system when the precondition on the time delay and the order of the disturbance model is satisfied. Based on the closed-loop non-parametric model (in terms of impulse response coefficients) that is estimated online by utilizing the one-shot closed-loop output data, the disturbance model is estimated by solving an optimization problem and hence the plant model is obtained. Subsequently, the new parameter set of the FPID controller is updated online by solving an optimization problem with respect to the H₂ norm of the resulting closed-loop transfer function. The benefit of the proposed scheme over the existing auto-tuning methods is the cost saving of the auto-tuning implementation due to the following facts: i) it does not rely on dual controllers or identification/exciting experiments; ii) it does not require prior knowledge of the process. The effectiveness of the proposed scheme is illustrated in terms of output variance index by numerical cases and industrial examples.